If he could see himself now, Harry would be horrified. Slack-mouthed, out for the count, he has got drips going into him, tubes coming out of him, wires and sensors everywhere you look. And now the final indignity: someone is taking the clippers to that rich golden fur.

"Poor thing," says a nurse. "He isn't half going to look weird."

There's worse to come. A neurosurgeon called Patrick Kenny is about to insert two stainless steel pins into Harry's skull. To these he will fit a clamp, immobilising Harry's head. His jaws will be wedged open. Then Kenny will cut a tiny hole through the back of the roof of Harry's mouth and, in an operation that will last more than four hours, set about removing a pea-sized tumour from a vital gland at the base of his brain.

Harry is a cat. A 12-year-old maine coon, in fact. He's a big old fella, as maine coons generally are, but Harry is considerably bigger than he should be, because the tumour on his pituitary gland is causing it to produce far more growth hormone than it should, a condition known as acromegaly. This has led to one of the disease's most common complications: uncontrolled diabetes, as the excess hormone counters the effects of insulin.

So Harry has needed insulin injections, and lots of them: 12 units, morning and night. It's miserable and according to Harry's owners, Richard and Tracy Mills, it's not making any appreciable difference. The options, says Stijn Niessen, lecturer in internal medicine at the Royal Veterinary College's Queen Mother hospital for animals (QMHA) near Potters Bar, Hertfordshire (which is where we are), are not plentiful.

"You can continue controlling the diabetes with insulin," says Niessen, as eight vets and nurses in surgical scrubs busy themselves purposefully around Harry, flat out on the table, "but that's a bit like mopping the floor with the tap turned on. The tumour continues to grow slowly – but there will eventually be a neurological impact."

There's radiation therapy, but that is long and tough: between five and 10 sessions, each requiring a general anaesthetic, and with no guarantee of success. There are also drugs called somatostatins, which inhibit the growth hormone, "but they're not generally very useful, at least not in cats".

Or there's this operation: "which is, well ... rather new."

In fact, it has been done a bare handful of times, and only once before in Britain, here at the QMHA. The risk, Niessen says, is very real: Harry could die. "But the owners," he says, "were of the opinion that it was better to attempt it. Not doing so would mean the tumour getting worse, Harry continuing to live with uncontrollable diabetes, and his quality of life being very poor – and deteriorating. And that's what it's about: quality of life for the animal. That's why we do this. That's why we're here."

Some people, of course, will question whether it is right for a shining, state-of-the-art institution like the QMHA, perhaps the finest of its kind in the world – open round the clock, 365 days a year, employing 200-plus highly qualified staff, with spacious consulting rooms, cutting-edge operating theatres, the latest in ECG, CT and MRI equipment, a hydrotherapy tank and even a blood donor programme – to be devoted to treating pet cats and dogs ("companion animals" is now the preferred term).

The QMHA treats up to 8,000 patients a year, most referred by their vets, for every conceivable condition: from acute heart failure to advanced neuromuscular disorders, malignant tumours to gastrointestinal disease, joint replacements to epilepsy. The array of disciplines offered here, says Holger Volk, genial head of the hospital's small animal group, is as complete as anyone could want: anaesthesia, cardiology, dermatology, emergency and critical care, internal medicine, neurology, oncology, opthalmology, orthopaedics, soft-tissue surgery.

To the uninformed visitor, it does indeed look more like a plush private healthcare facility for wealthy, or at least well-insured, humans. At reception, the only giveaway – in the temporary absence of any pets – is a polite but, one imagines, vitally important notice: "To ensure the safety of all patients, we would ask our clients to keep cats in their baskets and dogs on leads at all times."

This is plainly not an argument likely to be settled any time soon. Suffice it to say you won't find anyone here, staff or owner, who does not believe absolutely, like Niessen, that if an operation like the one now being performed on Harry can win the patient even a year or two of real quality of life, it is worth the £3,000-odd it will end up costing his owners' insurance company (some bills can be nearly twice as high).

But there is another good reason for doing this particular operation.

"What's fascinating is that this disease is quite rare in humans, but quite prevalent in cats," says Niessen. "And we still don't know what causes these tumours. Are there genetic factors? So these tumour cells will be cultured, and researchers will try to find out what's gone wrong with the gland. This operation could change the way we deal with this disease in people."

The concept of "one medicine" or "one health" – the idea that human and veterinary medicine are not divided, but can and should complement each other – is not new. Such giants of the profession as Rudolf Virchow, known as the father of modern pathology, and Sir William Osler, a founding professor at Johns Hopkins hospital and considered the inventor of modern medical teaching, both preached it, eloquently, in the 19th century.

But despite the fact that a number of diseases are shared by humans and animals, it has only lately begun to gain traction, spurred in particular by the similarities discovered recently between the gene profiles of humans and many animals. In 2007, the American Veterinary Medicine Association launched a drive "to unite human and veterinary medicine to improve animal and public health", while in Britain the Wellcome Trust is now funding five years of research at Imperial College into the historical convergences between human and animal medicine.

Niessen believes the communities can learn from each other. "Around 80% of diabetic cats have Type 2 diabetes – the condition that's costing the NHS £1m an hour," he says. "There are similarities between inflammatory bowel diseases in dogs and Crohn's disease, and between Cushing's disease and hyperthyroidism in cats. Cancers: lymphoma, leukemia. I could name you 100 diseases humans and animals share and the list would not be complete."

Human medicine, Niessen continues, puts "a lot of money and effort into trying to replicate these diseases, in mice for example. That can certainly help. But at best they're basically models – not the naturally occurring disease. And yet in cats and dogs we have those very diseases, occurring naturally."

Andy Lessey, the endocrinology researcher who arrives to take Harry's tumour off to the labs, agrees: "There's massive potential human application."

Some very respected human medics are already persuaded of the possible benefits of a more integrated – or at least a more collaborative – approach. Niessen works with Prof James Shaw, professor of regenerative medicine for diabetes at the University of Newcastle. He says doctor-vet collaboration is "only touching the surface at the moment" and could potentially prove "really very exciting".

Shaw says regenerative medicine – cell and tissue transplantation, gene therapy – in pets holds enormous promise, both in the benefits it can offer patients and in the development of therapies that may also work with humans. Rodents, he says, are not so helpful: "They're young, and good at repairing themselves. The circumstantial evidence is that what we see in mice isn't necessarily the same as what we see in humans."

Cats and dogs, on the other hand, look "much more like human patients. It's becoming increasingly clear that the diseases are very similar. And whereas regulations are just as stringent as for a regenerative medicine trial on a person, with companion animals it's more acceptable, simply because the risk-benefit is different."

Not, he emphasises, that this is "a cheap and cheerful way of doing animal testing. You're talking about real utility and benefit to an animal with a relatively short life who is unwell. Just like a human. The benefits to these animals will be there, clinically."

Hopefully, they will be for Harry. Kenny, the neurosurgeon, is now well into his operation, working with fierce precision, aided by a computer monitor displaying data and images from a prior CT scan of Harry's brain. Niessen, manning the IV lines, is "the hormone man. We're removing a tumour from an essential gland here. Harry will need cortisone infused, his glucose levels could be an issue, salt and water will be really important ... The potential for the patient to become unstable is very high."

For most of the owners whose animals are treated here, of course, "one medicine" means little. They are simply devoted to their pets, and want them to get better.

Nigel and Ros Gale from Whitstable have brought their seven-year old German shepherd for a checkup after surgery six weeks ago; Max has a serious immune-system disorder. "There's no cure," says Nigel. "It's about maintenance now." The couple are uninsured, and have spent £6,000 on their dog since he first fell ill. "But what," asks Nigel, "is the alternative? I certainly don't see one."

The Gales would not dream of having Max put down. Darren and Margaret Mangan from Uxbridge feel the same about Charlie, a three-year-old springer spaniel. Charlie very nearly died earlier this year: "Bleeding from his spinal cord, lost the use of back legs," says Darren. "Platelet count was at zero. Blood oozing from every orifice. He was put on steroids and they did his immune system in. Attacked his prostate, liver, kidneys."

After two weeks at the QMHA – and a bill of £5,500 – Charlie is now pretty much himself again. The Mangans, thankfully, were insured ("Best £12 a month I ever spent," says Darren). But "even if we hadn't been, you'd have to have paid. You'd have to have found a way of doing it. I can't understand people who don't. He's just such a lovely fellow. Our best mate. You couldn't ever get rid of him."

Like every owner I meet, Collette Parker, whose cat Henry has been hit by cars twice in 10 months, is beyond grateful to the hospital and its staff. "They're just brilliant," she says. "They call every day, even late in the evening, to keep you posted. They really, really care. Henry's had his leg pinned, he's had a bone graft, he's got an external leg frame. I think they must send the staff on a special cat-whispering course. They're just amazing."

They come, certainly, from around the world to work here. Clinical veterinary medicine in Britain is recognised as pretty much the best there is (there are almost as many specialists working here as in the whole of the rest of Europe), but this hospital in particular, says neurologist Birgit Parzefall, who has finally made it – after three attempts – to the QMHA from her native Germany, is seen as "exceptional". Stefano Cortellini from Rome, working in emergency and critical care, says it's "right at the top of everyone's list".

They come here, Niessen says, because "they want to make things better. Make untreatable illnesses treatable, and treatable illnesses curable." Most could probably earn more elsewhere: the QMHA is self-financing, and not for profit.

"I earn half what I could make in some places," says Volk frankly, watching two nurses take Alfie, a dachshund recovering from major spinal surgery to correct a disc problem, for a walk down the corridor in a supporting sling. "But people come, and stay, because it's cutting-edge. We're advancing veterinary science."

There's little doubt of that as far as Harry is concerned. A week after the op, I speak to his owners. The Millses only got Harry and his brother Milton in January; they had wanted, says Tracy, to "give a pair of oldies a home, because everyone always wants young ones". The couple are insured, and didn't think long about having the operation: "It's about quality of life," Tracy says. "He wouldn't have had much without it. And if it can benefit other cats, and even maybe humans, then so much the better."

Did it work? "He's fine," says Tracy. "He's eating more moderately, and his character's starting to come back – if you put your head down, on his level, he'll give you this affectionate little head-butt, like he used to."

More importantly, says Richard, the diabetes appears to have gone: "Harry's blood-sugar level seems to be at the right level, and he hasn't needed any insulin since the operation. None. It's been a complete success."

Harry, a 12-year-old maine coon, has a tumour on his pituitary gland, causing uncontrolled diabetes. In an attempt to save his life, his owners have opted for cutting-edge brain surgery at the Royal Veterinary College's Queen Mother hospital for animals